A326781 No position of a 1 in the reversed binary expansion of n is a power of 2.

0, 4, 16, 20, 32, 36, 48, 52, 64, 68, 80, 84, 96, 100, 112, 116, 256, 260, 272, 276, 288, 292, 304, 308, 320, 324, 336, 340, 352, 356, 368, 372, 512, 516, 528, 532, 544, 548, 560, 564, 576, 580, 592, 596, 608, 612, 624, 628, 768, 772, 784, 788, 800, 804, 816

Offset

1,2

Comments

Also BII-numbers (see A326031) of set-systems with no singleton edges. For example, the sequence of such set-systems together with their BII-numbers begins:

0: {}

4: {{1,2}}

16: {{1,3}}

20: {{1,2},{1,3}}

32: {{2,3}}

36: {{1,2},{2,3}}

48: {{1,3},{2,3}}

52: {{1,2},{1,3},{2,3}}

64: {{1,2,3}}

68: {{1,2},{1,2,3}}

80: {{1,3},{1,2,3}}

84: {{1,2},{1,3},{1,2,3}}

96: {{2,3},{1,2,3}}

100: {{1,2},{2,3},{1,2,3}}

112: {{1,3},{2,3},{1,2,3}}

116: {{1,2},{1,3},{2,3},{1,2,3}}

256: {{1,4}}

260: {{1,2},{1,4}}

272: {{1,3},{1,4}}

276: {{1,2},{1,3},{1,4}}

Links

Table of n, a(n) for n=1..55.

Formula

Conjectures from Colin Barker, Jul 27 2019: (Start)

G.f.: 4*x^2*(1 + 3*x + x^2 + 3*x^3 + x^4 + 3*x^5 + x^6 + 3*x^7 + x^8 + 3*x^9 + x^10 + 3*x^11 + x^12 + 3*x^13 + x^14 + 35*x^15) / ((1 - x)^2*(1 + x)*(1 + x^2)*(1 + x^4)*(1 + x^8)).

a(n) = a(n-1) + a(n-16) - a(n-17) for n>17.

(End)

Example

The binary indices of n are row n of A048793. The sequence of terms together with their binary indices begins:
    0: {}
    4: {3}
   16: {5}
   20: {3,5}
   32: {6}
   36: {3,6}
   48: {5,6}
   52: {3,5,6}
   64: {7}
   68: {3,7}
   80: {5,7}
   84: {3,5,7}
   96: {6,7}
  100: {3,6,7}
  112: {5,6,7}
  116: {3,5,6,7}
  256: {9}
  260: {3,9}
  272: {5,9}
  276: {3,5,9}

Mathematica

bpe[n_]:=Join@@Position[Reverse[IntegerDigits[n, 2]], 1];
Select[Range[100], !MemberQ[Length/@bpe/@bpe[#], 1]&]

Crossrefs

Cf. A000120, A029931, A048793, A062289, A070939, A326031, A326782, A326788.

Sequence in context: A216033 A071966 A349521 * A326788 A039943 A193996

Adjacent sequences: A326778 A326779 A326780 * A326782 A326783 A326784

Keyword

nonn,base

Author

Gus Wiseman, Jul 25 2019

Status

approved